Task

For each position i from w-1 to n-1, compute the z-score of x[i] relative to the window x[i-w+1 : i+1] (population std, ddof=0). If std = 0 for a window, output 0 for that position.

Input

• Line 1: two ints n w
• Line 2: n space-separated floats

Output

n - w + 1 space-separated floats (10 significant digits).

Example

Input:

6 3
1 3 5 4 2 6

Output:

1.069044968 0 -0.5345224838 1.069044968

Scaffolding

def rolling_zscore(x: list[float], w: int) -> list[float]: ...

Notes

Track A: the last element of each window is the point being scored. A spike shows as |z| > 2–3 — the basis of online anomaly detection.